Question

Metaculus Help: Spread the word

If you like Metaculus, tell your friends! Share this question via Facebook, Twitter, or Reddit.

Has Michael Atiyah possibly cracked the Riemann hypothesis?

The eminent mathematician Sir Michael Atiyah will be giving a talk on Monday 2018-09-24 at the Heidelberg Laureates' Forum in which, so it is claimed, he will be presenting a proof of the Riemann hypothesis. Here's an announcement from the HLF twitter account, and an article in New Scientist magazine.

The Riemann hypothesis is arguably the most important open problem in mathematics. Somewhere around a century ago, David Hilbert is said to have remarked that if he were to fall asleep for a thousand years, his first question on waking would be "Has anyone proved the Riemann hypothesis?". It is one of the Clay Mathematics Institute's millennium problems, with a $1M reward available for its solution.

Michael Atiyah is a very eminent mathematician indeed. He was awarded the Fields medal in 1966 and the Abel prize in 2004. He has been President of the Royal Society and Master of Trinity College, Cambridge. He is in these respects exactly the sort of person who should be solving famous open problems.

On the other hand, he is 89 years old, when mathematicians are generally well past their prime. A couple of years ago he published a paper claiming to prove another long-standing conjecture, namely that the 6-dimensional sphere admits no complex structure, and it seems to be generally felt that this paper does not come close to doing what it claims to do. Some mathematicians are quite outspoken in suggesting that Atiyah's recent history makes it unlikely that he really has a proof of the Riemann hypothesis.

So we ask: Does Atiyah have an actual proof of the Riemann hypothesis? Or at least something near enough to one that it remains only to patch up a few small holes?

to keep this question short term, we'll look at the reaction to Atiyah's lecture, with resolution as follows:

Two weeks after the lecture, we will collect all public statement by Fields-prize-winning mathematicians that express a firm opinion that either (a) Atiyah may well have proved the Riemann hypothesis, or (b) Atiyah's proof is fairly clearly flawed. The question will resolve positive if all firm statement are of type (a), negative if they are of type (b), and ambiguous if they are mixed or there are no such statement.

{{qctrl.predictionString()}}

Metaculus help: Predicting

Predictions are the heart of Metaculus. Predicting is how you contribute to the wisdom of the crowd, and how you earn points and build up your personal Metaculus track record.

The basics of predicting are very simple: move the slider to best match the likelihood of the outcome, and click predict. You can predict as often as you want, and you're encouraged to change your mind when new information becomes available.

The displayed score is split into current points and total points. Current points show how much your prediction is worth now, whereas total points show the combined worth of all of your predictions over the lifetime of the question. The scoring details are available on the FAQ.

Note: this question resolved before its original close time. All of your predictions came after the resolution, so you did not gain (or lose) any points for it.

Note: this question resolved before its original close time. You earned points up until the question resolution, but not afterwards.

Track your predictions

Continue exploring the site

Community Stats

Metaculus help: Community Stats

Use the community stats to get a better sense of the community consensus (or lack thereof) for this question. Sometimes people have wildly different ideas about the likely outcomes, and sometimes people are in close agreement. There are even times when the community seems very certain of uncertainty, like when everyone agrees that event is only 50% likely to happen.

When you make a prediction, check the community stats to see where you land. If your prediction is an outlier, might there be something you're overlooking that others have seen? Or do you have special insight that others are lacking? Either way, it might be a good idea to join the discussion in the comments.

Embed this question

You can use the below code snippet to embed this question on your own webpage. Feel free to change the height and width to suit your needs.